(20) (Textbook Delta Simulation) Assume a dealer sells calls on 10,000 shares, for $4 per call, or $40,000 total. The with strike price = $50. The Black-Scholes-Merton TOTAL fair value is $35,000, or $3.50 per call. The stock price is S = $52, the option Delta = .55 , and the WEEKLY interest rate is 1/10 % (NOT per year; 0.1 % per week). The dealer Delta Hedges the position.

(a) As in the first row of our books table what are Shares Purchased, Cost of Shares, Interest Cost ?

(b) The next week, Delta = .53 , and S = $ 51 . Finish the row as in the text, computing Shares Purchased or Sold, Cost of Shares, Cumulative Cost, and Interest Cost.

(c) Consider a full simulation as in the text. At expiration, the stock price ENDS at $ 47, and the Cumulative Cost is $ 38,000. CALCULATE the dealers overall profit or loss, AND explain (consider cumulative cost, initial option sale, and the option exercise at T if relevant).